# 







^ ft ^^^ 



TREASURY DEPARTMENT, 

OFFICE OF THE U. S. COAST AND GEODETIC SURVEY. 

u 
HENRY S. PRITCHETT, 

SUPERINTENDENT. 



TABLE OF FACTORS 



FOR 



COMPUTING DIFFERENCES IN ELEVATION 

(IN METERS) 



AND 



TABLE OF CORRECTIONS 



FOR 



CURVATURE AND REFRACTION 

(IN METERS). 



WASHINGTON: 

GOVERNMENT PRINTING OFFICE. 

1900. 



^-^'"i 



[Extract from the United States Coast and Geodetic Survey Report, 1897-98, App. No. 8.] 

Tad/e of factors for computing differences in elevation. 

To obtain the difference in elevation in meters multiply the horizontal distance in meters by the 
factor in this table corresponding to the observed angle of elevation or depression. The factors are 
given for each ten minutes, but the value of the nearest minute may be interpolated, using the column 
of differences for one minute. The result is still to be corrected where necessary for the effect of 
curvature and refraction. 

Table V. 



















Difference 


Angle 


0' 


10' 


20' 


30' 


40' 


50' 


60' 


for I min- 
ute (4th dec. 
place) 






Q-OGOO 


0*0029 


0-0058 


o-oo87 


o'oii6 


0-0I45 


0-0175 


29 


I 


■0175 


•0204 


•0233 


•0262 


•0291 


•0320 


■0349 


2-9 


2 


•0349 


•0378 


■0407 


■0437 


•0466 


■0495 


•0524 


2-9 


3 


•0524 


•0553 


•0582 


•0612 


•0641 


•0670 


•0699 


2-9 


4 


•0699 


•0729 


■0758 


■0787 


•0816 


•0846 


•0875 


2-9 


5 


•0875 


•090 t 


■0934 


•0963 


•0992 


•1022 


•105 1 


2-9 


6 


■I05I 


•1080 


•mo 


■1139 


•1169 


■I 198 


•1228 


2-9 


7 


■1228 


•1257 


•1287 


•1317 


•1346 


•1376 


•1405 


2-9 


8 


•1405 


■1435 


■1465 


■1495 


•1524 


•1554 


•1584 


3-0 


9 


•1584 


•1614 


■ '1644 


•1673 


•1703 


■1733 


•1763 


3"o 


ID 


•1763 


■1793 


•1823 


•1853 


■1883 


•1914 


•1944 


3"o 


II 


•1944 


•1974 


■2004 


■2035 


•2065 


•2095 


•2126 


3'o 


12 


•2126 


•2156 


■2186 


•2217 


•2247 


•2278 


•2309 


3-0 


13 


•2309 


•2339 


•2370 


■2401 


•2432 


■2462 


•2493 


3-1 


14 


■2493 


•2524 


■2555 


•2586 


•2617 


•2648 


•2679 


3-1 


15 


•2679 


•271I 


•2742 


•2773 


•2805 


•2836 


•2867 


3-1 


i5 


•2867 


•2899 


•2931 


•2962 


•2994 


•3026 


•3057 


3'2 


17 


•3057 


■30S9 


•3121 


•3153 


■3185 


•3217 


•3249 


3-2 


18 


•3249 


■3281 


■3314 


•3346 


•3378 


•3411 


■3443 


3"2 


19 


■3443 


■3476 


•3508 


•3541 


■3574 


•3607 


•3640 


3'3 


20 


•3640 


■3673 


•3706 


•3739 


■3772 


•3805 


•3839 


3"3 


21 


•3839 


■3872 


•3906 


■3939 


■3973 


•4006 


•4040 


3'3 


22 


•4040 


•4074 


•4108 


•4142 


•4176 


■4210 


■4245 


3-4 


23 


•4245 


■4279 


■4314 


•4348 


•4383 


■4417 


■4452 


3'4 


24 


•4452 


•4487 


■4522 


■4557 


■4592 


•4628 


•4663 


3-5 


25 


•4663 


■4699 


■4734 


•4770 


•4S06 


•4841 


•4877 


3'5 


26 


■4877 


■4913 


■4950 


•4986 


•5022 


■5059 


■5095 


3-6 


27 


■5095 


•5132 


■5169 


•5206 


•5243 


•5280 


■5317 


37 


28 


•5317 


■5354 


■5392 


■5430 


•5467 


■5505 


•5543 


3-8 


29 


■5543 


•5581 


■5619 


•565S 


•5696 


■5735 


•5774 


3-8 


30 


■5774 


•5812 


•5851 


•5890 


■5930 


■5969 


■6009 


3'9 


31 


■6009 


•6048 


•6088 


•6128 


■6168 


■620S 


•6249 


4-0 


32 


•6249 


•6289 


•6330 


■6371 


•6412 


•6453 


•6494 


4-1 


33 


•6494 


•6536 


•6577 


■5619 


•6661 


•6703 


■6745 


4-2 


34 


•6745 


•6787 


■6830 


•6873 


•6916 


•6959 


■7002 


4-3 


35 


•7002 


•7046 


•7089 


•7133 


•7177 


■7221 


■7265 


4-4 


36 


•7265 


•7310 


■7355 


•7400 


■7445 


•7490 


■7536 


4-5 


37 


■7536 


•7581 


•7627 


•7673 


•7720 


•7766 


•7813 


4-6 


38 


■7813 


•7860 


■7907 


•7954 


■S002 


■8050 


•8098 


47 


39 


•8098 


•8146 


•8195 


•8243 


•8292 


•8342 


•8391 


4-9 


40 


■8391 


•8441 


•8491 


•8541 


•8591 


•8642 


•8693 


5'o 


41 


•8693 


•8744 


•8796 


•8847 


•8899 


•8952 


•9004 


5'2 


42 


■9004 


•9057 


•9110 


•9163 


■9217 


■9271 


■9325 


5'4 


43 


■9325 


•9380 


•9435 


•9490 


•9545 


■9601 


■9657 


5-6 


44 


■9657 


■9713 


•9770 


■9827 


•9884 


•9942 


I '0000 


57 



/^-P-^/^ 



i 



[Extract from the United States Coast and Geodetic Survey Report, 1897-98, App. No. 8.] 

Table of corrections for curvature and refraction. 

The correction in meters for the combined effect of curvature and refraction is given for each icxd 
meters distance, the thousands of meters being given in the column to the left and the hundreds in 
the upper line. The correction is to be added to the difference of elevation for angles oi elevalion 
and substracted for angles of depression, or it is always to be added to the uncorrected elevation of 
the point to be determined from point of observation. 

Example: At a station whose elevation is 304 'So meters ( at telescope ), angle to signal 3° eleva- 
tion, horizontal distance 5 000 meters. From Table V factor is o'0524, which multiplied by 5 000 ^= 
262"oo. From Table VI correction is i'67 meters. Corrected difference of elevation = 262 '00 + 
i-67=263'67 meters, which added to 304"8o:= 568"47 meters for elevation of signal. If the above 
angle to signal be 3° depression, then corrected difference of elevation 262"oo — i'67 = 26o"33 meters, 
which makes height of signal = 304'8o — 26o"33 = 44"47 meters. 

TABtB Vl. 



Distance in 
meters 





100 


200 


300 


400 


500 


600 


700 


800 


900 


I 000 





coo 


0-00 


0-00 


Q-OI 


Q-OI 


0-02 


0-02 


0-03 


0-04 


0-05 


0-07 


I 000 


o'07 


0-08 


o-io 


o-ii 


0-13 


0-15 


0-17 


0-19 


0-22 


0-24 


0-27 


2 000 


0'27 


0-29 


0-32 


0-35 


0-38 


0-42 


0-45 


0-49 


0-52 


0-56 


0-60 


3 000 


o'6o 


0-64 


0-68 


o'73 


0-77 


0-82 


0-86 


0-91 


0-96 


I -01 


1-07 


4 000 


1-07 


1-12 


1-18 


1-23 


1-29 


1-35 


I -41 


1-47 


1-54 


I -60 


1-67 


5 000 


1-67 


1-74 


1-80 


1-87 


1-94 


2-02 


2-09 


2-17 


2-24 


2-32 


2-40 


6 000 


2-40 


2-48 


2-56 


2-65 


2-73 


2-82 


2-91 


3-00 


3-09 


3-18 


3-27 


7 000 


3'27 


3-36 


3-46 


3-55 


3-65 


3-75 


3-85 


3-96 


4-06 


4-16 


4-27 


8 000 


4-27 


4-38 


4-49 


4-60 


4-71 


4-82 


4-93 


5-05 


5-16 


5-28 


5-40 


9 000 


5 "40 


5-52 


5-65 


5-77 


5-89 


6-02 


6-15 


6-28 


6-41 


6-54 


6-67 


10 000 


6-67 


6-80 


6-94 


7-08 


7-22 


7-36 


7-50 


7-64 


7-78 


7-93 


8-07 


II 000 


8-07 


8-22 


8-37 


8-52 


8-67 


8-82 


8-98 


9-13 


9-29 


9-45 


9-61 


12 000 


9'6i 


977 


9-93 


10-09 


10-26 


10-42 


10-59 


10-76 


10-92 


II-IO 


11-27 


13 000 


II'27 


11-45 


11-62 


1 1 -80 


11-98 


12-16 


12-34 


12-52 


12-71 


12-89 


13-08 


14 000 


13-08 


13-26 


13-45 


13-64 


13-83 


14-03 


14-22 


14-42 


14-61 


14-81 


15-01 


15 000 


15-01 


15-21 


^5-41 


15-62 


15-82 


16-03 


16-24 


16-44 


16-65 


16-87 


17-08 


16 000 


17-08 


17-30 


17-51 


17-73 


17-95 


18-17 


18-39 


18-61 


18-83 


19-05 


19-28 


17 000 


19-28 


I9'5i 


19-73 


19-96 


20-19 


20-43 


20-66 


20-89 


21-13 


21-37 


21-61 


18 000 


21-61 


21-86 


22-10 


22-34 


22-58 


22-83 


23-08 


23-33 


23-58 


23-83 


24-08 


19 000 


24-08 


24-34 


24-60 


24-85 


25 -.11 


25-37 


25-63 


25-89 


26-15 


26-42 


26-68 



b 



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